Indeed, the Ran that we mentioned above already defined the annulment as the removal of leaven from one's mind, as stated earlier. This seems to follow the approach of the Tosafot, as this is his language. The concept of annulment is evident in the Gemara regarding the case where we say "the one checking needs to annul," as annulment is a legal declaration of ownerlessness. This is illustrated in the case of the fig tree, where it was touched by one who is deemed ownerless. Even though declaring something ownerless in this manner is not effective, as whoever says regarding his own possessions that they should be like dust does not actually make them ownerless, we still say "he annuls it in his heart" in the Gemara. Certainly, in terms of declaring something ownerless, doing so in one's heart is not effective, as matters of the heart are not considered valid actions. Furthermore, for one who says there in Nedarim according to Rabbi Yosei that ownerless property is like a gift, just as a gift only takes effect when it comes into the possession of the recipient and not when it is in the possession of the giver, the same applies to declaring something ownerless. Thus, how does the concept of annulment of leaven apply according to Rabbi Yosei, since it does not come into the possession of the one declaring it ownerless? The reason is that since with regards to something that is in the possession of an individual, he cannot declare it ownerless in this manner, leaven is different. This is because it is not in the possession of a person, but the Torah treats it as if it is in his possession. Therefore, since it is openly known that it is not desirable to him to have the merit of this leaven at all, it is effective even for well-known leaven, as we say in Moed Katan.